Working Seminar on Symplectic/Contact Geometry/Topology 

03/04/2012, 10:30 — 11:30 — Room P4.35, Mathematics Building
Daniele Sepe, CAMGSD/IST

Lecture VI - The Eliasson-Miranda-Zung linearisation theorem

The definition of non-degenerate singular orbits of completely integrable Hamiltonian systems gives local linear models for the underlying Hamiltonian ${ℝ}^n$-action. A natural question is whether there exists a symplectomorphism from an open neighbourhood of a fixed singular orbit to the local linear model which preserves the respective Lagrangian fibrations. The Eliasson-Miranda-Zung theorem answers the above questions affirmatively when the orbit is compact. In this lecture this theorem is stated and a strategy for its proof is outlined, so as to explain the main underlying geometric ideas.